Properties

Label 76.3.b.b.39.9
Level $76$
Weight $3$
Character 76.39
Analytic conductor $2.071$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 76.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07085000914\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + 448 x^{5} - 2688 x^{4} + 3584 x^{3} + 1024 x^{2} - 8192 x + 16384\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.9
Root \(0.711746 + 1.86907i\) of defining polynomial
Character \(\chi\) \(=\) 76.39
Dual form 76.3.b.b.39.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +O(q^{10})\) \(q+(0.711746 - 1.86907i) q^{2} -4.44946i q^{3} +(-2.98683 - 2.66060i) q^{4} +4.97973 q^{5} +(-8.31634 - 3.16688i) q^{6} +12.2628i q^{7} +(-7.09872 + 3.68892i) q^{8} -10.7977 q^{9} +(3.54430 - 9.30745i) q^{10} -13.4463i q^{11} +(-11.8382 + 13.2898i) q^{12} +14.1766 q^{13} +(22.9201 + 8.72803i) q^{14} -22.1571i q^{15} +(1.84237 + 15.8936i) q^{16} -5.89478 q^{17} +(-7.68520 + 20.1816i) q^{18} +4.35890i q^{19} +(-14.8736 - 13.2491i) q^{20} +54.5630 q^{21} +(-25.1320 - 9.57032i) q^{22} +0.906592i q^{23} +(16.4137 + 31.5855i) q^{24} -0.202335 q^{25} +(10.0901 - 26.4969i) q^{26} +7.99863i q^{27} +(32.6266 - 36.6271i) q^{28} -10.3853 q^{29} +(-41.4131 - 15.7702i) q^{30} +43.2608i q^{31} +(31.0175 + 7.86868i) q^{32} -59.8285 q^{33} +(-4.19559 + 11.0178i) q^{34} +61.0656i q^{35} +(32.2508 + 28.7283i) q^{36} -1.61331 q^{37} +(8.14708 + 3.10243i) q^{38} -63.0779i q^{39} +(-35.3497 + 18.3698i) q^{40} +69.3758 q^{41} +(38.8350 - 101.982i) q^{42} -32.0147i q^{43} +(-35.7752 + 40.1617i) q^{44} -53.7694 q^{45} +(1.69448 + 0.645264i) q^{46} +38.9732i q^{47} +(70.7178 - 8.19753i) q^{48} -101.377 q^{49} +(-0.144011 + 0.378179i) q^{50} +26.2286i q^{51} +(-42.3430 - 37.7182i) q^{52} -8.31560 q^{53} +(14.9500 + 5.69299i) q^{54} -66.9586i q^{55} +(-45.2367 - 87.0505i) q^{56} +19.3947 q^{57} +(-7.39169 + 19.4108i) q^{58} +20.9242i q^{59} +(-58.9512 + 66.1795i) q^{60} -118.329 q^{61} +(80.8574 + 30.7907i) q^{62} -132.410i q^{63} +(36.7837 - 52.3733i) q^{64} +70.5953 q^{65} +(-42.5827 + 111.824i) q^{66} +57.4499i q^{67} +(17.6067 + 15.6837i) q^{68} +4.03384 q^{69} +(114.136 + 43.4632i) q^{70} +11.3393i q^{71} +(76.6496 - 39.8318i) q^{72} -23.5952 q^{73} +(-1.14827 + 3.01539i) q^{74} +0.900282i q^{75} +(11.5973 - 13.0193i) q^{76} +164.889 q^{77} +(-117.897 - 44.8955i) q^{78} -0.286369i q^{79} +(9.17448 + 79.1456i) q^{80} -61.5894 q^{81} +(49.3780 - 129.668i) q^{82} -24.9311i q^{83} +(-162.971 - 145.171i) q^{84} -29.3544 q^{85} +(-59.8376 - 22.7863i) q^{86} +46.2089i q^{87} +(49.6022 + 95.4512i) q^{88} -43.7018 q^{89} +(-38.2702 + 100.499i) q^{90} +173.845i q^{91} +(2.41208 - 2.70784i) q^{92} +192.487 q^{93} +(72.8436 + 27.7390i) q^{94} +21.7061i q^{95} +(35.0113 - 138.011i) q^{96} +115.905 q^{97} +(-72.1549 + 189.481i) q^{98} +145.188i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} + O(q^{10}) \) \( 14q + 2q^{2} + 2q^{4} - 40q^{8} - 68q^{9} - 12q^{10} + 4q^{12} + 54q^{13} + 30q^{14} + 58q^{16} + 34q^{17} + 36q^{18} + 32q^{20} - 38q^{21} + 36q^{22} - 98q^{24} - 86q^{25} - 16q^{26} + 18q^{28} + 54q^{29} - 204q^{30} + 72q^{32} + 20q^{33} - 82q^{34} + 96q^{36} + 100q^{37} - 148q^{40} + 224q^{41} + 224q^{42} - 96q^{44} - 168q^{45} + 46q^{46} + 296q^{48} - 220q^{49} - 58q^{50} - 288q^{52} + 14q^{53} - 128q^{54} + 12q^{56} + 38q^{57} - 72q^{58} + 188q^{60} + 28q^{61} + 396q^{62} - 118q^{64} - 472q^{65} - 32q^{66} + 30q^{68} + 122q^{69} + 156q^{70} + 80q^{72} + 70q^{73} - 224q^{74} + 228q^{77} + 274q^{78} - 348q^{80} + 334q^{81} - 400q^{82} - 216q^{84} + 48q^{85} - 124q^{86} + 472q^{88} + 416q^{90} + 126q^{92} - 176q^{93} - 88q^{94} - 106q^{96} + 308q^{97} + 68q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.711746 1.86907i 0.355873 0.934534i
\(3\) 4.44946i 1.48315i −0.670869 0.741576i \(-0.734079\pi\)
0.670869 0.741576i \(-0.265921\pi\)
\(4\) −2.98683 2.66060i −0.746709 0.665151i
\(5\) 4.97973 0.995945 0.497973 0.867193i \(-0.334078\pi\)
0.497973 + 0.867193i \(0.334078\pi\)
\(6\) −8.31634 3.16688i −1.38606 0.527814i
\(7\) 12.2628i 1.75183i 0.482461 + 0.875917i \(0.339743\pi\)
−0.482461 + 0.875917i \(0.660257\pi\)
\(8\) −7.09872 + 3.68892i −0.887340 + 0.461116i
\(9\) −10.7977 −1.19974
\(10\) 3.54430 9.30745i 0.354430 0.930745i
\(11\) 13.4463i 1.22239i −0.791481 0.611193i \(-0.790690\pi\)
0.791481 0.611193i \(-0.209310\pi\)
\(12\) −11.8382 + 13.2898i −0.986520 + 1.10748i
\(13\) 14.1766 1.09050 0.545252 0.838272i \(-0.316434\pi\)
0.545252 + 0.838272i \(0.316434\pi\)
\(14\) 22.9201 + 8.72803i 1.63715 + 0.623431i
\(15\) 22.1571i 1.47714i
\(16\) 1.84237 + 15.8936i 0.115148 + 0.993348i
\(17\) −5.89478 −0.346752 −0.173376 0.984856i \(-0.555468\pi\)
−0.173376 + 0.984856i \(0.555468\pi\)
\(18\) −7.68520 + 20.1816i −0.426955 + 1.12120i
\(19\) 4.35890i 0.229416i
\(20\) −14.8736 13.2491i −0.743681 0.662454i
\(21\) 54.5630 2.59824
\(22\) −25.1320 9.57032i −1.14236 0.435014i
\(23\) 0.906592i 0.0394171i 0.999806 + 0.0197085i \(0.00627383\pi\)
−0.999806 + 0.0197085i \(0.993726\pi\)
\(24\) 16.4137 + 31.5855i 0.683905 + 1.31606i
\(25\) −0.202335 −0.00809341
\(26\) 10.0901 26.4969i 0.388081 1.01911i
\(27\) 7.99863i 0.296246i
\(28\) 32.6266 36.6271i 1.16524 1.30811i
\(29\) −10.3853 −0.358114 −0.179057 0.983839i \(-0.557305\pi\)
−0.179057 + 0.983839i \(0.557305\pi\)
\(30\) −41.4131 15.7702i −1.38044 0.525674i
\(31\) 43.2608i 1.39551i 0.716337 + 0.697755i \(0.245817\pi\)
−0.716337 + 0.697755i \(0.754183\pi\)
\(32\) 31.0175 + 7.86868i 0.969296 + 0.245896i
\(33\) −59.8285 −1.81299
\(34\) −4.19559 + 11.0178i −0.123400 + 0.324052i
\(35\) 61.0656i 1.74473i
\(36\) 32.2508 + 28.7283i 0.895857 + 0.798009i
\(37\) −1.61331 −0.0436030 −0.0218015 0.999762i \(-0.506940\pi\)
−0.0218015 + 0.999762i \(0.506940\pi\)
\(38\) 8.14708 + 3.10243i 0.214397 + 0.0816429i
\(39\) 63.0779i 1.61738i
\(40\) −35.3497 + 18.3698i −0.883742 + 0.459246i
\(41\) 69.3758 1.69209 0.846047 0.533109i \(-0.178976\pi\)
0.846047 + 0.533109i \(0.178976\pi\)
\(42\) 38.8350 101.982i 0.924643 2.42814i
\(43\) 32.0147i 0.744527i −0.928127 0.372264i \(-0.878582\pi\)
0.928127 0.372264i \(-0.121418\pi\)
\(44\) −35.7752 + 40.1617i −0.813072 + 0.912767i
\(45\) −53.7694 −1.19488
\(46\) 1.69448 + 0.645264i 0.0368366 + 0.0140275i
\(47\) 38.9732i 0.829217i 0.910000 + 0.414609i \(0.136082\pi\)
−0.910000 + 0.414609i \(0.863918\pi\)
\(48\) 70.7178 8.19753i 1.47329 0.170782i
\(49\) −101.377 −2.06893
\(50\) −0.144011 + 0.378179i −0.00288023 + 0.00756357i
\(51\) 26.2286i 0.514286i
\(52\) −42.3430 37.7182i −0.814289 0.725350i
\(53\) −8.31560 −0.156898 −0.0784491 0.996918i \(-0.524997\pi\)
−0.0784491 + 0.996918i \(0.524997\pi\)
\(54\) 14.9500 + 5.69299i 0.276852 + 0.105426i
\(55\) 66.9586i 1.21743i
\(56\) −45.2367 87.0505i −0.807798 1.55447i
\(57\) 19.3947 0.340258
\(58\) −7.39169 + 19.4108i −0.127443 + 0.334669i
\(59\) 20.9242i 0.354648i 0.984153 + 0.177324i \(0.0567440\pi\)
−0.984153 + 0.177324i \(0.943256\pi\)
\(60\) −58.9512 + 66.1795i −0.982520 + 1.10299i
\(61\) −118.329 −1.93983 −0.969913 0.243453i \(-0.921720\pi\)
−0.969913 + 0.243453i \(0.921720\pi\)
\(62\) 80.8574 + 30.7907i 1.30415 + 0.496624i
\(63\) 132.410i 2.10175i
\(64\) 36.7837 52.3733i 0.574745 0.818333i
\(65\) 70.5953 1.08608
\(66\) −42.5827 + 111.824i −0.645193 + 1.69430i
\(67\) 57.4499i 0.857462i 0.903432 + 0.428731i \(0.141039\pi\)
−0.903432 + 0.428731i \(0.858961\pi\)
\(68\) 17.6067 + 15.6837i 0.258923 + 0.230642i
\(69\) 4.03384 0.0584615
\(70\) 114.136 + 43.4632i 1.63051 + 0.620903i
\(71\) 11.3393i 0.159709i 0.996807 + 0.0798545i \(0.0254456\pi\)
−0.996807 + 0.0798545i \(0.974554\pi\)
\(72\) 76.6496 39.8318i 1.06458 0.553219i
\(73\) −23.5952 −0.323222 −0.161611 0.986855i \(-0.551669\pi\)
−0.161611 + 0.986855i \(0.551669\pi\)
\(74\) −1.14827 + 3.01539i −0.0155171 + 0.0407485i
\(75\) 0.900282i 0.0120038i
\(76\) 11.5973 13.0193i 0.152596 0.171307i
\(77\) 164.889 2.14142
\(78\) −117.897 44.8955i −1.51150 0.575583i
\(79\) 0.286369i 0.00362492i −0.999998 0.00181246i \(-0.999423\pi\)
0.999998 0.00181246i \(-0.000576925\pi\)
\(80\) 9.17448 + 79.1456i 0.114681 + 0.989320i
\(81\) −61.5894 −0.760363
\(82\) 49.3780 129.668i 0.602170 1.58132i
\(83\) 24.9311i 0.300375i −0.988658 0.150188i \(-0.952012\pi\)
0.988658 0.150188i \(-0.0479878\pi\)
\(84\) −162.971 145.171i −1.94013 1.72822i
\(85\) −29.3544 −0.345346
\(86\) −59.8376 22.7863i −0.695786 0.264957i
\(87\) 46.2089i 0.531137i
\(88\) 49.6022 + 95.4512i 0.563662 + 1.08467i
\(89\) −43.7018 −0.491031 −0.245515 0.969393i \(-0.578957\pi\)
−0.245515 + 0.969393i \(0.578957\pi\)
\(90\) −38.2702 + 100.499i −0.425224 + 1.11665i
\(91\) 173.845i 1.91038i
\(92\) 2.41208 2.70784i 0.0262183 0.0294331i
\(93\) 192.487 2.06975
\(94\) 72.8436 + 27.7390i 0.774932 + 0.295096i
\(95\) 21.7061i 0.228485i
\(96\) 35.0113 138.011i 0.364702 1.43761i
\(97\) 115.905 1.19490 0.597448 0.801908i \(-0.296182\pi\)
0.597448 + 0.801908i \(0.296182\pi\)
\(98\) −72.1549 + 189.481i −0.736275 + 1.93348i
\(99\) 145.188i 1.46655i
\(100\) 0.604342 + 0.538334i 0.00604342 + 0.00538334i
\(101\) −10.3010 −0.101990 −0.0509950 0.998699i \(-0.516239\pi\)
−0.0509950 + 0.998699i \(0.516239\pi\)
\(102\) 49.0230 + 18.6681i 0.480618 + 0.183021i
\(103\) 110.807i 1.07579i −0.843011 0.537897i \(-0.819219\pi\)
0.843011 0.537897i \(-0.180781\pi\)
\(104\) −100.635 + 52.2962i −0.967648 + 0.502848i
\(105\) 271.709 2.58770
\(106\) −5.91860 + 15.5424i −0.0558358 + 0.146627i
\(107\) 29.6484i 0.277088i −0.990356 0.138544i \(-0.955758\pi\)
0.990356 0.138544i \(-0.0442422\pi\)
\(108\) 21.2812 23.8906i 0.197048 0.221209i
\(109\) −1.00851 −0.00925235 −0.00462617 0.999989i \(-0.501473\pi\)
−0.00462617 + 0.999989i \(0.501473\pi\)
\(110\) −125.150 47.6576i −1.13773 0.433251i
\(111\) 7.17835i 0.0646698i
\(112\) −194.900 + 22.5927i −1.74018 + 0.201720i
\(113\) −59.0375 −0.522456 −0.261228 0.965277i \(-0.584127\pi\)
−0.261228 + 0.965277i \(0.584127\pi\)
\(114\) 13.8041 36.2501i 0.121089 0.317983i
\(115\) 4.51458i 0.0392572i
\(116\) 31.0192 + 27.6312i 0.267407 + 0.238200i
\(117\) −153.074 −1.30832
\(118\) 39.1088 + 14.8927i 0.331431 + 0.126210i
\(119\) 72.2868i 0.607452i
\(120\) 81.7358 + 157.287i 0.681131 + 1.31072i
\(121\) −59.8017 −0.494229
\(122\) −84.2205 + 221.166i −0.690332 + 1.81283i
\(123\) 308.685i 2.50963i
\(124\) 115.100 129.213i 0.928225 1.04204i
\(125\) −125.501 −1.00401
\(126\) −247.484 94.2424i −1.96416 0.747955i
\(127\) 209.454i 1.64925i −0.565681 0.824624i \(-0.691387\pi\)
0.565681 0.824624i \(-0.308613\pi\)
\(128\) −71.7086 106.028i −0.560224 0.828341i
\(129\) −142.448 −1.10425
\(130\) 50.2460 131.948i 0.386507 1.01498i
\(131\) 46.0795i 0.351752i −0.984412 0.175876i \(-0.943724\pi\)
0.984412 0.175876i \(-0.0562758\pi\)
\(132\) 178.698 + 159.180i 1.35377 + 1.20591i
\(133\) −53.4525 −0.401899
\(134\) 107.378 + 40.8898i 0.801327 + 0.305147i
\(135\) 39.8310i 0.295044i
\(136\) 41.8454 21.7454i 0.307687 0.159893i
\(137\) 206.272 1.50564 0.752819 0.658228i \(-0.228694\pi\)
0.752819 + 0.658228i \(0.228694\pi\)
\(138\) 2.87107 7.53953i 0.0208049 0.0546343i
\(139\) 125.355i 0.901835i −0.892566 0.450918i \(-0.851097\pi\)
0.892566 0.450918i \(-0.148903\pi\)
\(140\) 162.471 182.393i 1.16051 1.30281i
\(141\) 173.410 1.22986
\(142\) 21.1940 + 8.07073i 0.149253 + 0.0568361i
\(143\) 190.621i 1.33302i
\(144\) −19.8933 171.613i −0.138148 1.19176i
\(145\) −51.7159 −0.356661
\(146\) −16.7938 + 44.1011i −0.115026 + 0.302062i
\(147\) 451.074i 3.06853i
\(148\) 4.81869 + 4.29238i 0.0325587 + 0.0290026i
\(149\) −170.871 −1.14679 −0.573394 0.819280i \(-0.694374\pi\)
−0.573394 + 0.819280i \(0.694374\pi\)
\(150\) 1.68269 + 0.640772i 0.0112179 + 0.00427182i
\(151\) 131.745i 0.872482i 0.899830 + 0.436241i \(0.143690\pi\)
−0.899830 + 0.436241i \(0.856310\pi\)
\(152\) −16.0796 30.9426i −0.105787 0.203570i
\(153\) 63.6499 0.416012
\(154\) 117.359 308.189i 0.762074 2.00123i
\(155\) 215.427i 1.38985i
\(156\) −167.825 + 188.403i −1.07580 + 1.20771i
\(157\) −3.40126 −0.0216641 −0.0108320 0.999941i \(-0.503448\pi\)
−0.0108320 + 0.999941i \(0.503448\pi\)
\(158\) −0.535243 0.203822i −0.00338761 0.00129001i
\(159\) 36.9999i 0.232704i
\(160\) 154.459 + 39.1839i 0.965366 + 0.244899i
\(161\) −11.1174 −0.0690522
\(162\) −43.8360 + 115.115i −0.270593 + 0.710585i
\(163\) 170.519i 1.04613i 0.852293 + 0.523064i \(0.175211\pi\)
−0.852293 + 0.523064i \(0.824789\pi\)
\(164\) −207.214 184.582i −1.26350 1.12550i
\(165\) −297.930 −1.80563
\(166\) −46.5980 17.7446i −0.280711 0.106895i
\(167\) 245.186i 1.46818i −0.679053 0.734089i \(-0.737610\pi\)
0.679053 0.734089i \(-0.262390\pi\)
\(168\) −387.327 + 201.279i −2.30552 + 1.19809i
\(169\) 31.9746 0.189199
\(170\) −20.8929 + 54.8654i −0.122899 + 0.322738i
\(171\) 47.0659i 0.275239i
\(172\) −85.1784 + 95.6225i −0.495223 + 0.555945i
\(173\) 62.3081 0.360162 0.180081 0.983652i \(-0.442364\pi\)
0.180081 + 0.983652i \(0.442364\pi\)
\(174\) 86.3676 + 32.8890i 0.496366 + 0.189017i
\(175\) 2.48121i 0.0141783i
\(176\) 213.709 24.7729i 1.21426 0.140755i
\(177\) 93.1014 0.525997
\(178\) −31.1046 + 81.6816i −0.174745 + 0.458885i
\(179\) 129.080i 0.721115i −0.932737 0.360557i \(-0.882586\pi\)
0.932737 0.360557i \(-0.117414\pi\)
\(180\) 160.600 + 143.059i 0.892224 + 0.794773i
\(181\) −198.677 −1.09766 −0.548831 0.835933i \(-0.684927\pi\)
−0.548831 + 0.835933i \(0.684927\pi\)
\(182\) 324.928 + 123.733i 1.78532 + 0.679854i
\(183\) 526.501i 2.87706i
\(184\) −3.34435 6.43565i −0.0181758 0.0349763i
\(185\) −8.03384 −0.0434261
\(186\) 137.002 359.771i 0.736569 1.93426i
\(187\) 79.2628i 0.423865i
\(188\) 103.692 116.407i 0.551555 0.619184i
\(189\) −98.0860 −0.518973
\(190\) 40.5702 + 15.4492i 0.213528 + 0.0813118i
\(191\) 380.217i 1.99067i 0.0965041 + 0.995333i \(0.469234\pi\)
−0.0965041 + 0.995333i \(0.530766\pi\)
\(192\) −233.033 163.667i −1.21371 0.852434i
\(193\) −264.689 −1.37145 −0.685724 0.727862i \(-0.740514\pi\)
−0.685724 + 0.727862i \(0.740514\pi\)
\(194\) 82.4948 216.634i 0.425231 1.11667i
\(195\) 314.111i 1.61082i
\(196\) 302.797 + 269.725i 1.54488 + 1.37615i
\(197\) 125.565 0.637386 0.318693 0.947858i \(-0.396756\pi\)
0.318693 + 0.947858i \(0.396756\pi\)
\(198\) 271.367 + 103.337i 1.37054 + 0.521904i
\(199\) 14.4081i 0.0724026i 0.999345 + 0.0362013i \(0.0115258\pi\)
−0.999345 + 0.0362013i \(0.988474\pi\)
\(200\) 1.43632 0.746400i 0.00718161 0.00373200i
\(201\) 255.621 1.27175
\(202\) −7.33168 + 19.2532i −0.0362955 + 0.0953131i
\(203\) 127.353i 0.627356i
\(204\) 69.7839 78.3405i 0.342078 0.384022i
\(205\) 345.473 1.68523
\(206\) −207.105 78.8663i −1.00537 0.382846i
\(207\) 9.78908i 0.0472902i
\(208\) 26.1184 + 225.316i 0.125569 + 1.08325i
\(209\) 58.6109 0.280435
\(210\) 193.388 507.842i 0.920893 2.41830i
\(211\) 81.1242i 0.384475i 0.981348 + 0.192237i \(0.0615744\pi\)
−0.981348 + 0.192237i \(0.938426\pi\)
\(212\) 24.8373 + 22.1245i 0.117157 + 0.104361i
\(213\) 50.4539 0.236873
\(214\) −55.4148 21.1021i −0.258948 0.0986080i
\(215\) 159.424i 0.741508i
\(216\) −29.5063 56.7800i −0.136603 0.262871i
\(217\) −530.500 −2.44470
\(218\) −0.717800 + 1.88497i −0.00329266 + 0.00864664i
\(219\) 104.986i 0.479388i
\(220\) −178.150 + 199.994i −0.809775 + 0.909066i
\(221\) −83.5677 −0.378134
\(222\) 13.4168 + 5.10916i 0.0604362 + 0.0230142i
\(223\) 181.944i 0.815892i −0.913006 0.407946i \(-0.866245\pi\)
0.913006 0.407946i \(-0.133755\pi\)
\(224\) −96.4924 + 380.363i −0.430770 + 1.69805i
\(225\) 2.18475 0.00970999
\(226\) −42.0197 + 110.345i −0.185928 + 0.488253i
\(227\) 423.077i 1.86377i −0.362748 0.931887i \(-0.618162\pi\)
0.362748 0.931887i \(-0.381838\pi\)
\(228\) −57.9289 51.6017i −0.254074 0.226323i
\(229\) 360.509 1.57427 0.787137 0.616778i \(-0.211562\pi\)
0.787137 + 0.616778i \(0.211562\pi\)
\(230\) 8.43806 + 3.21324i 0.0366872 + 0.0139706i
\(231\) 733.668i 3.17605i
\(232\) 73.7223 38.3106i 0.317769 0.165132i
\(233\) 2.13039 0.00914329 0.00457164 0.999990i \(-0.498545\pi\)
0.00457164 + 0.999990i \(0.498545\pi\)
\(234\) −108.950 + 286.105i −0.465596 + 1.22267i
\(235\) 194.076i 0.825855i
\(236\) 55.6711 62.4972i 0.235894 0.264819i
\(237\) −1.27419 −0.00537631
\(238\) −135.109 51.4499i −0.567685 0.216176i
\(239\) 228.926i 0.957847i 0.877857 + 0.478924i \(0.158973\pi\)
−0.877857 + 0.478924i \(0.841027\pi\)
\(240\) 352.155 40.8214i 1.46731 0.170089i
\(241\) 245.133 1.01715 0.508575 0.861017i \(-0.330172\pi\)
0.508575 + 0.861017i \(0.330172\pi\)
\(242\) −42.5636 + 111.774i −0.175883 + 0.461874i
\(243\) 346.027i 1.42398i
\(244\) 353.430 + 314.828i 1.44848 + 1.29028i
\(245\) −504.831 −2.06054
\(246\) −576.953 219.705i −2.34534 0.893110i
\(247\) 61.7942i 0.250179i
\(248\) −159.586 307.096i −0.643491 1.23829i
\(249\) −110.930 −0.445502
\(250\) −89.3246 + 234.569i −0.357299 + 0.938278i
\(251\) 178.193i 0.709934i −0.934879 0.354967i \(-0.884492\pi\)
0.934879 0.354967i \(-0.115508\pi\)
\(252\) −352.291 + 395.487i −1.39798 + 1.56939i
\(253\) 12.1903 0.0481829
\(254\) −391.485 149.078i −1.54128 0.586923i
\(255\) 130.611i 0.512201i
\(256\) −249.211 + 58.5636i −0.973482 + 0.228764i
\(257\) −239.267 −0.930998 −0.465499 0.885048i \(-0.654125\pi\)
−0.465499 + 0.885048i \(0.654125\pi\)
\(258\) −101.387 + 266.245i −0.392972 + 1.03196i
\(259\) 19.7838i 0.0763852i
\(260\) −210.857 187.826i −0.810987 0.722409i
\(261\) 112.137 0.429643
\(262\) −86.1257 32.7969i −0.328724 0.125179i
\(263\) 39.7564i 0.151165i −0.997140 0.0755825i \(-0.975918\pi\)
0.997140 0.0755825i \(-0.0240816\pi\)
\(264\) 424.706 220.703i 1.60873 0.835996i
\(265\) −41.4094 −0.156262
\(266\) −38.0446 + 99.9064i −0.143025 + 0.375588i
\(267\) 194.449i 0.728274i
\(268\) 152.852 171.593i 0.570342 0.640274i
\(269\) −25.6332 −0.0952905 −0.0476453 0.998864i \(-0.515172\pi\)
−0.0476453 + 0.998864i \(0.515172\pi\)
\(270\) 74.4468 + 28.3495i 0.275729 + 0.104998i
\(271\) 53.7535i 0.198353i 0.995070 + 0.0991763i \(0.0316208\pi\)
−0.995070 + 0.0991763i \(0.968379\pi\)
\(272\) −10.8604 93.6892i −0.0399278 0.344446i
\(273\) 773.515 2.83339
\(274\) 146.813 385.537i 0.535816 1.40707i
\(275\) 2.72065i 0.00989328i
\(276\) −12.0484 10.7325i −0.0436537 0.0388857i
\(277\) 353.449 1.27599 0.637995 0.770040i \(-0.279764\pi\)
0.637995 + 0.770040i \(0.279764\pi\)
\(278\) −234.297 89.2210i −0.842796 0.320939i
\(279\) 467.116i 1.67425i
\(280\) −225.266 433.488i −0.804523 1.54817i
\(281\) 221.272 0.787445 0.393722 0.919229i \(-0.371187\pi\)
0.393722 + 0.919229i \(0.371187\pi\)
\(282\) 123.424 324.115i 0.437673 1.14934i
\(283\) 81.0003i 0.286220i −0.989707 0.143110i \(-0.954290\pi\)
0.989707 0.143110i \(-0.0457103\pi\)
\(284\) 30.1695 33.8687i 0.106231 0.119256i
\(285\) 96.5804 0.338879
\(286\) −356.285 135.674i −1.24575 0.474385i
\(287\) 850.745i 2.96427i
\(288\) −334.916 84.9634i −1.16290 0.295012i
\(289\) −254.252 −0.879763
\(290\) −36.8086 + 96.6606i −0.126926 + 0.333312i
\(291\) 515.714i 1.77221i
\(292\) 70.4750 + 62.7776i 0.241353 + 0.214992i
\(293\) 517.659 1.76675 0.883377 0.468664i \(-0.155264\pi\)
0.883377 + 0.468664i \(0.155264\pi\)
\(294\) 843.089 + 321.050i 2.86765 + 1.09201i
\(295\) 104.197i 0.353210i
\(296\) 11.4524 5.95138i 0.0386906 0.0201060i
\(297\) 107.552 0.362127
\(298\) −121.617 + 319.371i −0.408111 + 1.07171i
\(299\) 12.8524i 0.0429845i
\(300\) 2.39529 2.68899i 0.00798432 0.00896331i
\(301\) 392.591 1.30429
\(302\) 246.240 + 93.7688i 0.815364 + 0.310493i
\(303\) 45.8338i 0.151267i
\(304\) −69.2785 + 8.03069i −0.227890 + 0.0264167i
\(305\) −589.248 −1.93196
\(306\) 45.3026 118.966i 0.148048 0.388778i
\(307\) 249.101i 0.811405i 0.914005 + 0.405703i \(0.132973\pi\)
−0.914005 + 0.405703i \(0.867027\pi\)
\(308\) −492.497 438.705i −1.59902 1.42437i
\(309\) −493.030 −1.59557
\(310\) 402.648 + 153.329i 1.29886 + 0.494610i
\(311\) 252.481i 0.811835i −0.913910 0.405917i \(-0.866952\pi\)
0.913910 0.405917i \(-0.133048\pi\)
\(312\) 232.690 + 447.773i 0.745801 + 1.43517i
\(313\) −595.875 −1.90376 −0.951878 0.306478i \(-0.900849\pi\)
−0.951878 + 0.306478i \(0.900849\pi\)
\(314\) −2.42083 + 6.35719i −0.00770966 + 0.0202458i
\(315\) 659.366i 2.09322i
\(316\) −0.761914 + 0.855337i −0.00241112 + 0.00270676i
\(317\) 491.836 1.55153 0.775766 0.631020i \(-0.217364\pi\)
0.775766 + 0.631020i \(0.217364\pi\)
\(318\) 69.1554 + 26.3345i 0.217470 + 0.0828130i
\(319\) 139.643i 0.437753i
\(320\) 183.173 260.805i 0.572414 0.815014i
\(321\) −131.919 −0.410963
\(322\) −7.91277 + 20.7792i −0.0245738 + 0.0645316i
\(323\) 25.6948i 0.0795504i
\(324\) 183.957 + 163.865i 0.567770 + 0.505756i
\(325\) −2.86842 −0.00882590
\(326\) 318.711 + 121.366i 0.977643 + 0.372289i
\(327\) 4.48730i 0.0137226i
\(328\) −492.480 + 255.922i −1.50146 + 0.780251i
\(329\) −477.923 −1.45265
\(330\) −212.050 + 556.851i −0.642576 + 1.68743i
\(331\) 413.971i 1.25067i 0.780358 + 0.625333i \(0.215037\pi\)
−0.780358 + 0.625333i \(0.784963\pi\)
\(332\) −66.3319 + 74.4652i −0.199795 + 0.224293i
\(333\) 17.4200 0.0523122
\(334\) −458.269 174.510i −1.37206 0.522485i
\(335\) 286.085i 0.853985i
\(336\) 100.525 + 867.201i 0.299182 + 2.58096i
\(337\) 393.328 1.16715 0.583573 0.812061i \(-0.301654\pi\)
0.583573 + 0.812061i \(0.301654\pi\)
\(338\) 22.7578 59.7627i 0.0673307 0.176813i
\(339\) 262.685i 0.774882i
\(340\) 87.6768 + 78.1005i 0.257873 + 0.229707i
\(341\) 581.696 1.70585
\(342\) −87.9695 33.4990i −0.257221 0.0979503i
\(343\) 642.295i 1.87258i
\(344\) 118.100 + 227.263i 0.343313 + 0.660649i
\(345\) 20.0874 0.0582244
\(346\) 44.3475 116.458i 0.128172 0.336584i
\(347\) 476.716i 1.37382i −0.726742 0.686911i \(-0.758966\pi\)
0.726742 0.686911i \(-0.241034\pi\)
\(348\) 122.944 138.018i 0.353286 0.396605i
\(349\) −118.794 −0.340383 −0.170191 0.985411i \(-0.554439\pi\)
−0.170191 + 0.985411i \(0.554439\pi\)
\(350\) −4.63754 1.76599i −0.0132501 0.00504568i
\(351\) 113.393i 0.323057i
\(352\) 105.804 417.069i 0.300580 1.18485i
\(353\) 297.291 0.842185 0.421092 0.907018i \(-0.361647\pi\)
0.421092 + 0.907018i \(0.361647\pi\)
\(354\) 66.2646 174.013i 0.187188 0.491562i
\(355\) 56.4668i 0.159061i
\(356\) 130.530 + 116.273i 0.366657 + 0.326610i
\(357\) −321.637 −0.900944
\(358\) −241.259 91.8719i −0.673907 0.256625i
\(359\) 212.978i 0.593252i 0.954994 + 0.296626i \(0.0958615\pi\)
−0.954994 + 0.296626i \(0.904139\pi\)
\(360\) 381.694 198.351i 1.06026 0.550976i
\(361\) −19.0000 −0.0526316
\(362\) −141.407 + 371.341i −0.390628 + 1.02580i
\(363\) 266.085i 0.733017i
\(364\) 462.532 519.246i 1.27069 1.42650i
\(365\) −117.498 −0.321912
\(366\) 984.067 + 374.735i 2.68871 + 1.02387i
\(367\) 326.797i 0.890456i 0.895417 + 0.445228i \(0.146877\pi\)
−0.895417 + 0.445228i \(0.853123\pi\)
\(368\) −14.4090 + 1.67028i −0.0391549 + 0.00453879i
\(369\) −749.097 −2.03007
\(370\) −5.71805 + 15.0158i −0.0154542 + 0.0405832i
\(371\) 101.973i 0.274860i
\(372\) −574.927 512.132i −1.54550 1.37670i
\(373\) 235.813 0.632205 0.316103 0.948725i \(-0.397626\pi\)
0.316103 + 0.948725i \(0.397626\pi\)
\(374\) 148.148 + 56.4150i 0.396116 + 0.150842i
\(375\) 558.410i 1.48909i
\(376\) −143.769 276.660i −0.382365 0.735798i
\(377\) −147.228 −0.390524
\(378\) −69.8123 + 183.329i −0.184689 + 0.484998i
\(379\) 471.811i 1.24489i −0.782666 0.622443i \(-0.786140\pi\)
0.782666 0.622443i \(-0.213860\pi\)
\(380\) 57.7514 64.8326i 0.151977 0.170612i
\(381\) −931.959 −2.44609
\(382\) 710.652 + 270.618i 1.86034 + 0.708424i
\(383\) 131.099i 0.342294i −0.985246 0.171147i \(-0.945253\pi\)
0.985246 0.171147i \(-0.0547473\pi\)
\(384\) −471.766 + 319.064i −1.22856 + 0.830897i
\(385\) 821.104 2.13274
\(386\) −188.392 + 494.722i −0.488061 + 1.28166i
\(387\) 345.684i 0.893239i
\(388\) −346.189 308.377i −0.892239 0.794786i
\(389\) 20.4959 0.0526887 0.0263444 0.999653i \(-0.491613\pi\)
0.0263444 + 0.999653i \(0.491613\pi\)
\(390\) −587.095 223.567i −1.50537 0.573249i
\(391\) 5.34417i 0.0136679i
\(392\) 719.650 373.973i 1.83584 0.954014i
\(393\) −205.029 −0.521702
\(394\) 89.3704 234.690i 0.226828 0.595659i
\(395\) 1.42604i 0.00361022i
\(396\) 386.288 433.653i 0.975475 1.09508i
\(397\) 9.07740 0.0228650 0.0114325 0.999935i \(-0.496361\pi\)
0.0114325 + 0.999935i \(0.496361\pi\)
\(398\) 26.9298 + 10.2549i 0.0676628 + 0.0257661i
\(399\) 237.835i 0.596077i
\(400\) −0.372776 3.21583i −0.000931939 0.00803958i
\(401\) −336.682 −0.839606 −0.419803 0.907615i \(-0.637901\pi\)
−0.419803 + 0.907615i \(0.637901\pi\)
\(402\) 181.937 477.773i 0.452580 1.18849i
\(403\) 613.289i 1.52181i
\(404\) 30.7673 + 27.4068i 0.0761568 + 0.0678387i
\(405\) −306.698 −0.757280
\(406\) −238.032 90.6432i −0.586286 0.223259i
\(407\) 21.6930i 0.0532997i
\(408\) −96.7553 186.189i −0.237145 0.456347i
\(409\) 75.6667 0.185004 0.0925020 0.995712i \(-0.470514\pi\)
0.0925020 + 0.995712i \(0.470514\pi\)
\(410\) 245.889 645.712i 0.599729 1.57491i
\(411\) 917.800i 2.23309i
\(412\) −294.813 + 330.961i −0.715565 + 0.803304i
\(413\) −256.591 −0.621285
\(414\) −18.2965 6.96734i −0.0441944 0.0168293i
\(415\) 124.150i 0.299157i
\(416\) 439.721 + 111.551i 1.05702 + 0.268151i
\(417\) −557.762 −1.33756
\(418\) 41.7160 109.548i 0.0997992 0.262076i
\(419\) 619.532i 1.47860i 0.673378 + 0.739298i \(0.264843\pi\)
−0.673378 + 0.739298i \(0.735157\pi\)
\(420\) −811.549 722.910i −1.93226 1.72121i
\(421\) −18.4384 −0.0437967 −0.0218983 0.999760i \(-0.506971\pi\)
−0.0218983 + 0.999760i \(0.506971\pi\)
\(422\) 151.627 + 57.7398i 0.359305 + 0.136824i
\(423\) 420.820i 0.994846i
\(424\) 59.0301 30.6756i 0.139222 0.0723482i
\(425\) 1.19272 0.00280641
\(426\) 35.9104 94.3018i 0.0842966 0.221366i
\(427\) 1451.05i 3.39825i
\(428\) −78.8826 + 88.5548i −0.184305 + 0.206904i
\(429\) −848.162 −1.97707
\(430\) −297.975 113.470i −0.692965 0.263883i
\(431\) 496.147i 1.15115i 0.817748 + 0.575577i \(0.195222\pi\)
−0.817748 + 0.575577i \(0.804778\pi\)
\(432\) −127.127 + 14.7364i −0.294275 + 0.0341121i
\(433\) 623.687 1.44039 0.720193 0.693774i \(-0.244053\pi\)
0.720193 + 0.693774i \(0.244053\pi\)
\(434\) −377.582 + 991.542i −0.870004 + 2.28466i
\(435\) 230.108i 0.528983i
\(436\) 3.01224 + 2.68324i 0.00690881 + 0.00615421i
\(437\) −3.95174 −0.00904289
\(438\) 196.226 + 74.7233i 0.448004 + 0.170601i
\(439\) 105.337i 0.239947i 0.992777 + 0.119974i \(0.0382810\pi\)
−0.992777 + 0.119974i \(0.961719\pi\)
\(440\) 247.005 + 475.321i 0.561376 + 1.08027i
\(441\) 1094.64 2.48217
\(442\) −59.4790 + 156.194i −0.134568 + 0.353380i
\(443\) 113.329i 0.255821i 0.991786 + 0.127911i \(0.0408271\pi\)
−0.991786 + 0.127911i \(0.959173\pi\)
\(444\) 19.0987 21.4405i 0.0430152 0.0482895i
\(445\) −217.623 −0.489040
\(446\) −340.066 129.498i −0.762479 0.290354i
\(447\) 760.285i 1.70086i
\(448\) 642.246 + 451.072i 1.43358 + 1.00686i
\(449\) 413.979 0.922003 0.461001 0.887399i \(-0.347490\pi\)
0.461001 + 0.887399i \(0.347490\pi\)
\(450\) 1.55499 4.08345i 0.00345553 0.00907432i
\(451\) 932.845i 2.06839i
\(452\) 176.335 + 157.076i 0.390122 + 0.347512i
\(453\) 586.192 1.29402
\(454\) −790.760 301.123i −1.74176 0.663267i
\(455\) 865.700i 1.90264i
\(456\) −137.678 + 71.5457i −0.301925 + 0.156898i
\(457\) 320.223 0.700707 0.350353 0.936618i \(-0.386061\pi\)
0.350353 + 0.936618i \(0.386061\pi\)
\(458\) 256.591 673.816i 0.560242 1.47121i
\(459\) 47.1502i 0.102724i
\(460\) 12.0115 13.4843i 0.0261120 0.0293137i
\(461\) −460.179 −0.998218 −0.499109 0.866539i \(-0.666339\pi\)
−0.499109 + 0.866539i \(0.666339\pi\)
\(462\) −1371.28 522.185i −2.96813 1.13027i
\(463\) 323.224i 0.698108i −0.937103 0.349054i \(-0.886503\pi\)
0.937103 0.349054i \(-0.113497\pi\)
\(464\) −19.1335 165.059i −0.0412360 0.355732i
\(465\) 958.533 2.06136
\(466\) 1.51629 3.98184i 0.00325385 0.00854472i
\(467\) 523.352i 1.12067i −0.828267 0.560334i \(-0.810673\pi\)
0.828267 0.560334i \(-0.189327\pi\)
\(468\) 457.206 + 407.268i 0.976935 + 0.870232i
\(469\) −704.500 −1.50213
\(470\) 362.741 + 138.133i 0.771790 + 0.293900i
\(471\) 15.1338i 0.0321311i
\(472\) −77.1879 148.535i −0.163534 0.314693i
\(473\) −430.477 −0.910100
\(474\) −0.906897 + 2.38154i −0.00191328 + 0.00502435i
\(475\) 0.881959i 0.00185676i
\(476\) −192.327 + 215.909i −0.404048 + 0.453590i
\(477\) 89.7891 0.188237
\(478\) 427.878 + 162.937i 0.895141 + 0.340872i
\(479\) 458.055i 0.956274i −0.878285 0.478137i \(-0.841312\pi\)
0.878285 0.478137i \(-0.158688\pi\)
\(480\) 174.347 687.256i 0.363223 1.43178i
\(481\) −22.8712 −0.0475492
\(482\) 174.473 458.171i 0.361977 0.950562i
\(483\) 49.4664i 0.102415i
\(484\) 178.618 + 159.109i 0.369045 + 0.328737i
\(485\) 577.174 1.19005
\(486\) 646.748 + 246.283i 1.33076 + 0.506756i
\(487\) 49.8747i 0.102412i −0.998688 0.0512060i \(-0.983693\pi\)
0.998688 0.0512060i \(-0.0163065\pi\)
\(488\) 839.987 436.508i 1.72128 0.894484i
\(489\) 758.716 1.55157
\(490\) −359.312 + 943.565i −0.733289 + 1.92564i
\(491\) 381.364i 0.776709i −0.921510 0.388354i \(-0.873044\pi\)
0.921510 0.388354i \(-0.126956\pi\)
\(492\) −821.288 + 921.990i −1.66928 + 1.87396i
\(493\) 61.2191 0.124177
\(494\) 115.498 + 43.9817i 0.233801 + 0.0890319i
\(495\) 722.997i 1.46060i
\(496\) −687.569 + 79.7022i −1.38623 + 0.160690i
\(497\) −139.053 −0.279784
\(498\) −78.9540 + 207.336i −0.158542 + 0.416337i
\(499\) 191.567i 0.383903i 0.981404 + 0.191951i \(0.0614816\pi\)
−0.981404 + 0.191951i \(0.938518\pi\)
\(500\) 374.850 + 333.908i 0.749700 + 0.667816i
\(501\) −1090.94 −2.17753
\(502\) −333.056 126.829i −0.663458 0.252646i
\(503\) 393.811i 0.782925i 0.920194 + 0.391463i \(0.128031\pi\)
−0.920194 + 0.391463i \(0.871969\pi\)
\(504\) 488.451 + 939.942i 0.969148 + 1.86496i
\(505\) −51.2961 −0.101576
\(506\) 8.67638 22.7845i 0.0171470 0.0450286i
\(507\) 142.270i 0.280611i
\(508\) −557.276 + 625.606i −1.09700 + 1.23151i
\(509\) −711.118 −1.39709 −0.698544 0.715567i \(-0.746168\pi\)
−0.698544 + 0.715567i \(0.746168\pi\)
\(510\) 244.121 + 92.9620i 0.478669 + 0.182278i
\(511\) 289.345i 0.566232i
\(512\) −67.9159 + 507.476i −0.132648 + 0.991163i
\(513\) −34.8652 −0.0679634
\(514\) −170.297 + 447.206i −0.331317 + 0.870050i
\(515\) 551.787i 1.07143i
\(516\) 425.468 + 378.997i 0.824551 + 0.734491i
\(517\) 524.044 1.01362
\(518\) −36.9772 14.0810i −0.0713846 0.0271834i
\(519\) 277.237i 0.534176i
\(520\) −501.137 + 260.421i −0.963724 + 0.500809i
\(521\) 401.456 0.770549 0.385274 0.922802i \(-0.374107\pi\)
0.385274 + 0.922802i \(0.374107\pi\)
\(522\) 79.8130 209.592i 0.152898 0.401516i
\(523\) 83.5113i 0.159677i 0.996808 + 0.0798387i \(0.0254405\pi\)
−0.996808 + 0.0798387i \(0.974559\pi\)
\(524\) −122.599 + 137.632i −0.233968 + 0.262656i
\(525\) −11.0400 −0.0210286
\(526\) −74.3074 28.2965i −0.141269 0.0537956i
\(527\) 255.013i 0.483896i
\(528\) −110.226 950.889i −0.208761 1.80093i
\(529\) 528.178 0.998446
\(530\) −29.4730 + 77.3970i −0.0556094 + 0.146032i
\(531\) 225.933i 0.425486i
\(532\) 159.654 + 142.216i 0.300101 + 0.267323i
\(533\) 983.510 1.84523
\(534\) 363.439 + 138.398i 0.680597 + 0.259173i
\(535\) 147.641i 0.275964i
\(536\) −211.928 407.821i −0.395389 0.760860i
\(537\) −574.334 −1.06952
\(538\) −18.2443 + 47.9101i −0.0339113 + 0.0890523i
\(539\) 1363.15i 2.52903i
\(540\) 105.975 118.969i 0.196249 0.220312i
\(541\) 315.779 0.583694 0.291847 0.956465i \(-0.405730\pi\)
0.291847 + 0.956465i \(0.405730\pi\)
\(542\) 100.469 + 38.2589i 0.185367 + 0.0705883i
\(543\) 884.004i 1.62800i
\(544\) −182.841 46.3842i −0.336105 0.0852650i
\(545\) −5.02208 −0.00921483
\(546\) 550.546 1445.75i 1.00833 2.64790i
\(547\) 115.726i 0.211564i −0.994389 0.105782i \(-0.966265\pi\)
0.994389 0.105782i \(-0.0337346\pi\)
\(548\) −616.101 548.809i −1.12427 1.00148i
\(549\) 1277.68 2.32729
\(550\) 5.08508 + 1.93641i 0.00924561 + 0.00352075i
\(551\) 45.2684i 0.0821569i
\(552\) −28.6351 + 14.8805i −0.0518752 + 0.0269575i
\(553\) 3.51170 0.00635027
\(554\) 251.566 660.621i 0.454091 1.19246i
\(555\) 35.7462i 0.0644076i
\(556\) −333.520 + 374.415i −0.599857 + 0.673408i
\(557\) −597.571 −1.07284 −0.536419 0.843952i \(-0.680223\pi\)
−0.536419 + 0.843952i \(0.680223\pi\)
\(558\) −873.071 332.468i −1.56464 0.595820i
\(559\) 453.857i 0.811910i
\(560\) −970.551 + 112.505i −1.73313 + 0.200902i
\(561\) 352.676 0.628656
\(562\) 157.490 413.573i 0.280230 0.735894i
\(563\) 622.336i 1.10539i 0.833383 + 0.552696i \(0.186401\pi\)
−0.833383 + 0.552696i \(0.813599\pi\)
\(564\) −517.946 461.375i −0.918344 0.818040i
\(565\) −293.991 −0.520337
\(566\) −151.395 57.6516i −0.267482 0.101858i
\(567\) 755.261i 1.33203i
\(568\) −41.8300 80.4948i −0.0736443 0.141716i
\(569\) 497.207 0.873826 0.436913 0.899504i \(-0.356072\pi\)
0.436913 + 0.899504i \(0.356072\pi\)
\(570\) 68.7408 180.515i 0.120598 0.316694i
\(571\) 623.096i 1.09124i 0.838034 + 0.545619i \(0.183705\pi\)
−0.838034 + 0.545619i \(0.816295\pi\)
\(572\) −507.168 + 569.355i −0.886658 + 0.995376i
\(573\) 1691.76 2.95246
\(574\) 1590.10 + 605.514i 2.77021 + 1.05490i
\(575\) 0.183436i 0.000319019i
\(576\) −397.178 + 565.509i −0.689545 + 0.981787i
\(577\) −934.139 −1.61896 −0.809479 0.587148i \(-0.800251\pi\)
−0.809479 + 0.587148i \(0.800251\pi\)
\(578\) −180.963 + 475.214i −0.313084 + 0.822169i
\(579\) 1177.72i 2.03406i
\(580\) 154.467 + 137.596i 0.266322 + 0.237234i
\(581\) 305.727 0.526208
\(582\) −963.904 367.057i −1.65619 0.630682i
\(583\) 111.814i 0.191790i
\(584\) 167.496 87.0410i 0.286808 0.149043i
\(585\) −762.265 −1.30302
\(586\) 368.442 967.540i 0.628740 1.65109i
\(587\) 778.304i 1.32590i −0.748663 0.662951i \(-0.769304\pi\)
0.748663 0.662951i \(-0.230696\pi\)
\(588\) 1200.13 1347.28i 2.04104 2.29130i
\(589\) −188.569 −0.320152
\(590\) 194.751 + 74.1617i 0.330087 + 0.125698i
\(591\) 558.696i 0.945340i
\(592\) −2.97231 25.6412i −0.00502079 0.0433129i
\(593\) −1012.64 −1.70766 −0.853832 0.520549i \(-0.825727\pi\)
−0.853832 + 0.520549i \(0.825727\pi\)
\(594\) 76.5494 201.021i 0.128871 0.338420i
\(595\) 359.969i 0.604989i
\(596\) 510.365 + 454.621i 0.856317 + 0.762788i
\(597\) 64.1083 0.107384
\(598\) 24.0219 + 9.14761i 0.0401705 + 0.0152970i
\(599\) 37.3119i 0.0622903i −0.999515 0.0311452i \(-0.990085\pi\)
0.999515 0.0311452i \(-0.00991541\pi\)
\(600\) −3.32107 6.39085i −0.00553512 0.0106514i
\(601\) −181.988 −0.302808 −0.151404 0.988472i \(-0.548379\pi\)
−0.151404 + 0.988472i \(0.548379\pi\)
\(602\) 279.425 733.779i 0.464161 1.21890i
\(603\) 620.325i 1.02873i
\(604\) 350.521 393.500i 0.580332 0.651490i
\(605\) −297.796 −0.492225
\(606\) 85.6665 + 32.6220i 0.141364 + 0.0538317i
\(607\) 218.379i 0.359767i 0.983688 + 0.179884i \(0.0575721\pi\)
−0.983688 + 0.179884i \(0.942428\pi\)
\(608\) −34.2988 + 135.202i −0.0564125 + 0.222372i
\(609\) −566.653 −0.930464
\(610\) −419.395 + 1101.34i −0.687532 + 1.80548i
\(611\) 552.506i 0.904265i
\(612\) −190.112 169.347i −0.310640 0.276711i
\(613\) 641.406 1.04634 0.523170 0.852229i \(-0.324749\pi\)
0.523170 + 0.852229i \(0.324749\pi\)
\(614\) 465.588 + 177.297i 0.758286 + 0.288757i
\(615\) 1537.17i 2.49946i
\(616\) −1170.50 + 608.264i −1.90017 + 0.987442i
\(617\) −223.015 −0.361450 −0.180725 0.983534i \(-0.557844\pi\)
−0.180725 + 0.983534i \(0.557844\pi\)
\(618\) −350.912 + 921.506i −0.567819 + 1.49111i
\(619\) 126.536i 0.204420i 0.994763 + 0.102210i \(0.0325914\pi\)
−0.994763 + 0.102210i \(0.967409\pi\)
\(620\) 573.166 643.445i 0.924461 1.03781i
\(621\) −7.25150 −0.0116771
\(622\) −471.903 179.702i −0.758687 0.288910i
\(623\) 535.908i 0.860205i
\(624\) 1002.53 116.213i 1.60663 0.186238i
\(625\) −619.901 −0.991841
\(626\) −424.112 + 1113.73i −0.677495 + 1.77912i
\(627\) 260.786i 0.415927i
\(628\) 10.1590 + 9.04941i 0.0161768 + 0.0144099i
\(629\) 9.51011 0.0151194
\(630\) −1232.40 469.301i −1.95619 0.744922i
\(631\) 250.558i 0.397081i 0.980093 + 0.198541i \(0.0636202\pi\)
−0.980093 + 0.198541i \(0.936380\pi\)
\(632\) 1.05639 + 2.03285i 0.00167151 + 0.00321654i
\(633\) 360.959 0.570235
\(634\) 350.062 919.275i 0.552149 1.44996i
\(635\) 1043.03i 1.64256i
\(636\) 98.4421 110.513i 0.154783 0.173762i
\(637\) −1437.18 −2.25617
\(638\) 261.003 + 99.3906i 0.409095 + 0.155785i
\(639\) 122.438i 0.191609i
\(640\) −357.089 527.989i −0.557952 0.824982i
\(641\) −744.927 −1.16213 −0.581067 0.813856i \(-0.697364\pi\)
−0.581067 + 0.813856i \(0.697364\pi\)
\(642\) −93.8929 + 246.566i −0.146251 + 0.384059i
\(643\) 1161.89i 1.80699i 0.428604 + 0.903493i \(0.359006\pi\)
−0.428604 + 0.903493i \(0.640994\pi\)
\(644\) 33.2058 + 29.5790i 0.0515619 + 0.0459301i
\(645\) −709.351 −1.09977
\(646\) −48.0253 18.2882i −0.0743425 0.0283098i
\(647\) 550.347i 0.850614i −0.905049 0.425307i \(-0.860166\pi\)
0.905049 0.425307i \(-0.139834\pi\)
\(648\) 437.206 227.199i 0.674701 0.350615i
\(649\) 281.352 0.433517
\(650\) −2.04158 + 5.36127i −0.00314090 + 0.00824810i
\(651\) 2360.44i 3.62587i
\(652\) 453.683 509.312i 0.695833 0.781153i
\(653\) −170.874 −0.261675 −0.130838 0.991404i \(-0.541767\pi\)
−0.130838 + 0.991404i \(0.541767\pi\)
\(654\) 8.38708 + 3.19382i 0.0128243 + 0.00488352i
\(655\) 229.463i 0.350326i
\(656\) 127.816 + 1102.63i 0.194841 + 1.68084i
\(657\) 254.773 0.387783
\(658\) −340.160 + 893.270i −0.516960 + 1.35755i
\(659\) 933.406i 1.41640i −0.706013 0.708199i \(-0.749508\pi\)
0.706013 0.708199i \(-0.250492\pi\)
\(660\) 889.867 + 792.673i 1.34828 + 1.20102i
\(661\) −498.493 −0.754150 −0.377075 0.926183i \(-0.623070\pi\)
−0.377075 + 0.926183i \(0.623070\pi\)
\(662\) 773.740 + 294.642i 1.16879 + 0.445079i
\(663\) 371.831i 0.560831i
\(664\) 91.9691 + 176.979i 0.138508 + 0.266535i
\(665\) −266.179 −0.400269
\(666\) 12.3986 32.5591i 0.0186165 0.0488876i
\(667\) 9.41523i 0.0141158i
\(668\) −652.342 + 732.329i −0.976560 + 1.09630i
\(669\) −809.551 −1.21009
\(670\) 534.712 + 203.620i 0.798078 + 0.303910i
\(671\) 1591.09i 2.37122i
\(672\) 1692.41 + 429.339i 2.51846 + 0.638897i
\(673\) 779.779 1.15866 0.579331 0.815093i \(-0.303314\pi\)
0.579331 + 0.815093i \(0.303314\pi\)
\(674\) 279.950 735.157i 0.415356 1.09074i
\(675\) 1.61841i 0.00239764i
\(676\) −95.5028 85.0718i −0.141276 0.125846i
\(677\) 910.302 1.34461 0.672306 0.740273i \(-0.265304\pi\)
0.672306 + 0.740273i \(0.265304\pi\)
\(678\) 490.976 + 186.965i 0.724154 + 0.275760i
\(679\) 1421.32i 2.09326i
\(680\) 208.379 108.286i 0.306439 0.159244i
\(681\) −1882.46 −2.76426
\(682\) 414.020 1087.23i 0.607067 1.59418i
\(683\) 93.5131i 0.136915i −0.997654 0.0684576i \(-0.978192\pi\)
0.997654 0.0684576i \(-0.0218078\pi\)
\(684\) −125.224 + 140.578i −0.183076 + 0.205524i
\(685\) 1027.18 1.49953
\(686\) −1200.49 457.151i −1.74999 0.666401i
\(687\) 1604.07i 2.33489i
\(688\) 508.827 58.9827i 0.739575 0.0857307i
\(689\) −117.887 −0.171098
\(690\) 14.2972 37.5448i 0.0207205 0.0544127i
\(691\) 663.683i 0.960468i 0.877140 + 0.480234i \(0.159448\pi\)
−0.877140 + 0.480234i \(0.840552\pi\)
\(692\) −186.104 165.777i −0.268936 0.239562i
\(693\) −1780.42 −2.56915
\(694\) −891.015 339.301i −1.28388 0.488906i
\(695\) 624.234i 0.898179i
\(696\) −170.461 328.024i −0.244916 0.471299i
\(697\) −408.956 −0.586737
\(698\) −84.5509 + 222.033i −0.121133 + 0.318099i
\(699\) 9.47906i 0.0135609i
\(700\) −6.60151 + 7.41095i −0.00943073 + 0.0105871i
\(701\) 959.216 1.36835 0.684177 0.729316i \(-0.260162\pi\)
0.684177 + 0.729316i \(0.260162\pi\)
\(702\) 211.939 + 80.7070i 0.301908 + 0.114967i
\(703\) 7.03225i 0.0100032i
\(704\) −704.225 494.603i −1.00032 0.702560i
\(705\) 863.532 1.22487
\(706\) 211.596 555.658i 0.299711 0.787051i
\(707\) 126.319i 0.178670i
\(708\) −278.079 247.706i −0.392766 0.349867i
\(709\) 825.957 1.16496 0.582480 0.812845i \(-0.302082\pi\)
0.582480 + 0.812845i \(0.302082\pi\)
\(710\) 105.540 + 40.1900i 0.148648 + 0.0566056i
\(711\) 3.09212i 0.00434897i
\(712\) 310.227 161.212i 0.435711 0.226422i
\(713\) −39.2199 −0.0550069
\(714\) −228.924 + 601.162i −0.320622 + 0.841963i
\(715\) 949.243i 1.32761i
\(716\) −343.430 + 385.539i −0.479650 + 0.538463i
\(717\) 1018.59 1.42063
\(718\) 398.070 + 151.586i 0.554414 + 0.211122i
\(719\) 1019.44i 1.41786i −0.705281 0.708928i \(-0.749179\pi\)
0.705281 0.708928i \(-0.250821\pi\)
\(720\) −99.0630 854.588i −0.137587 1.18693i
\(721\) 1358.81 1.88461
\(722\) −13.5232 + 35.5123i −0.0187302 + 0.0491860i
\(723\) 1090.71i 1.50859i
\(724\) 593.415 + 528.601i 0.819634 + 0.730111i
\(725\) 2.10131 0.00289836
\(726\) 497.331 + 189.385i 0.685030 + 0.260861i
\(727\) 227.791i 0.313330i 0.987652 + 0.156665i \(0.0500742\pi\)
−0.987652 + 0.156665i \(0.949926\pi\)
\(728\) −641.301 1234.08i −0.880907 1.69516i
\(729\) 985.328 1.35162
\(730\) −83.6286 + 219.611i −0.114560 + 0.300837i
\(731\) 188.720i 0.258166i
\(732\) 1400.81 1572.57i 1.91368 2.14832i
\(733\) −998.335 −1.36198 −0.680992 0.732291i \(-0.738451\pi\)
−0.680992 + 0.732291i \(0.738451\pi\)
\(734\) 610.807 + 232.597i 0.832162 + 0.316889i
\(735\) 2246.23i 3.05609i
\(736\) −7.13369 + 28.1202i −0.00969251 + 0.0382068i
\(737\) 772.486 1.04815
\(738\) −533.167 + 1400.11i −0.722448 + 1.89717i
\(739\) 614.741i 0.831856i 0.909398 + 0.415928i \(0.136543\pi\)
−0.909398 + 0.415928i \(0.863457\pi\)
\(740\) 23.9957 + 21.3749i 0.0324267 + 0.0288850i
\(741\) 274.950 0.371053
\(742\) −190.594 72.5788i −0.256866 0.0978151i
\(743\) 156.926i 0.211206i −0.994408 0.105603i \(-0.966323\pi\)
0.994408 0.105603i \(-0.0336772\pi\)
\(744\) −1366.41 + 710.070i −1.83657 + 0.954395i
\(745\) −850.893 −1.14214
\(746\) 167.839 440.750i 0.224985 0.590817i
\(747\) 269.198i 0.360372i
\(748\) 210.887 236.745i 0.281934 0.316504i
\(749\) 363.573 0.485412
\(750\) 1043.71 + 397.446i 1.39161 + 0.529928i
\(751\) 766.925i 1.02120i −0.859817 0.510602i \(-0.829422\pi\)
0.859817 0.510602i \(-0.170578\pi\)
\(752\) −619.424 + 71.8030i −0.823702 + 0.0954827i
\(753\) −792.864 −1.05294
\(754\) −104.789 + 275.179i −0.138977 + 0.364958i
\(755\) 656.053i 0.868944i
\(756\) 292.967 + 260.968i 0.387522 + 0.345196i
\(757\) 163.896 0.216507 0.108253 0.994123i \(-0.465474\pi\)
0.108253 + 0.994123i \(0.465474\pi\)
\(758\) −881.848 335.810i −1.16339 0.443021i
\(759\) 54.2401i 0.0714626i
\(760\) −80.0722 154.086i −0.105358 0.202744i
\(761\) −512.227 −0.673098 −0.336549 0.941666i \(-0.609260\pi\)
−0.336549 + 0.941666i \(0.609260\pi\)
\(762\) −663.318 + 1741.89i −0.870496 + 2.28595i
\(763\) 12.3672i 0.0162086i
\(764\) 1011.61 1135.65i 1.32409 1.48645i
\(765\) 316.959 0.414326
\(766\) −245.032 93.3089i −0.319886 0.121813i
\(767\) 296.633i 0.386745i
\(768\) 260.576 + 1108.86i 0.339292 + 1.44382i
\(769\) 1124.70 1.46255 0.731275 0.682083i \(-0.238926\pi\)
0.731275 + 0.682083i \(0.238926\pi\)
\(770\) 584.417 1534.70i 0.758983 1.99312i
\(771\) 1064.61i 1.38081i
\(772\) 790.583 + 704.234i 1.02407 + 0.912220i
\(773\) 669.217 0.865740 0.432870 0.901456i \(-0.357501\pi\)
0.432870 + 0.901456i \(0.357501\pi\)
\(774\) 646.106 + 246.039i 0.834763 + 0.317880i
\(775\) 8.75319i 0.0112944i
\(776\) −822.776 + 427.564i −1.06028 + 0.550985i
\(777\) −88.0270 −0.113291
\(778\) 14.5879 38.3083i 0.0187505 0.0492394i
\(779\) 302.402i 0.388193i